Abstract

Let A0
be a closed,
minimal symmetric operator from a Hilbert space ℍ
into
ℍ with domain not dense in ℍ. Let
A^
also be a correct selfadjoint extension of A0.
The purpose of this paper is (1) to characterize, with the help of
A^, all the correct selfadjoint extensions B of
A0 with domain equal to D(A^), (2)
to give the solution of their corresponding problems, (3) to find
sufficient conditions for B
to be positive (definite) when
A^ is positive (definite).